Coal is a porous medium with fractal characteristics. In order to investigate the effect of fractal dimensions on methane adsorption capacity, fractal characteristics of 11 coal samples were analyzed, using scanning electron microscopy (SEM) and low-pressure nitrogen gas adsorption (LP-N(2)GA). Data from SEM image analysis and LP-N2GA experiments were applied to assess the heterogeneities of pore distribution (D-1) and the irregularities of coal surface (D-2) on the basis of box-counting method and Frenkel-Halsey-Hill (FHH) theory, respectively. The relationship between fractal dimensions and coalification was investigated. Based on the physical description of fractal surfaces and pore distributions, the influence of fractal dimensions (both D-1 and D-2) on CH4 adsorption characteristics was also discussed. The results indicate that these coal samples have different CH4 adsorption characteristics and fractal geometries, with D-1 ranging between 1.5380 and 1.8267, and D-2 varying from 2.2656 to 2.6541. The U-shaped curve relationship between D values (including D-1 and D-2) and volatile matter (V-daf) is observed, demonstrating that coalification makes coal surfaces and pore networks comparatively smoother and more regular for lower rank coals (V-daf > 15%), but rougher and more complex for higher rank coals (V-daf< 15%). The Langmuir volume (V-L) shows a positive linear correlation with the fractal dimension D-2 values, but little correlation with D-1 values. While, the Langmuir pressure (P-L) is affected by both D-1 and D-2. Fractal dimensions comprehensively reflect the difference in physical properties of coal, which can be used to evaluate CH4 adsorption capacity. Fractal analysis is of great significance for better understanding of the surface irregularity and methane storage capacity of a coal reservoir. (C) 2016 Elsevier Ltd. All rights reserved.